Propability of finding a particle outside the classical limit

[Noctisdark]

Homework Statement

I'm asked to calculate the propability of finding a particle outside the classical limit for a quantum harmonic oscillator in it's ground state

Homework Equations

Ψ0(x) = a*e^mωx2/2hbar
When a = (mω/πhbar)^1/4
The ground state energy E0 =hbar*ω²/2

The Attempt at a Solution

I actually don't know what to do, I've tried to consider it as tunelling by finding when the energy is equal to the potential
E0 = hbar*ω²/2 = mω²x², and stuck there !
And thank for your assistance

 

[TSny]

You might start by finding the amplitude, $A$, of oscillation for a classical oscillator with energy E0. The quantum oscillator is "outside the classical limit" when x is outside the range $-A\leq x \leq A$.

E0 = hbar*ω²/2 = mω²x²

I don't understand this equation. Why is $\omega$ squared in the middle expression. I also don't understand the meaning of the expression on the right.

I think you have a typo in the expression for the wavefunction. The argument of the exponential should be negative.